Left-Handed Metamaterials for Microwave Engineering Applications. Department of Electrical Engineering UCLA

Size: px

Start display at page:

Download "Left-Handed Metamaterials for Microwave Engineering Applications. Department of Electrical Engineering UCLA"

Pauline Perkins
5 years ago
Views:

1 Left-Handed Metamaterials for Microwave Engineering Applications Department of Electrical Engineering UCLA

2 Outline Left-Handed Metamaterial Introduction Resonant approach Transmission line approach Composite Right/Left-Handed Metamaterial Metamaterial-Based Microwave Devices Dominant leaky-wave antenna Small, resonant backward wave antennas Dual-band hybrid coupler Negative refractive index flat lens Future Trends Summary

3 What is a Left-Handed Metamaterial? μ plasma air wire structure air (Permeability) reflected conventional refracted (RH) air ε < 0, μ > 0 No transmission LHMs ε < 0, μ < 0 air incident ε > 0, μ > 0 n εμ =+ ferrites split rings structure ε (Permittivity) n = εμ ε > 0, μ < 0 No transmission 1967: Veselago speculates about the possibility of LHMs and discusses their properties.

4 What is a Left-Handed Metamaterial? Veselago s Conclusions Simultaneous negative permittivity (-ε) and permeability (-μ). Reversal of Snell s Law (negative index of refraction), Doppler Effect, and Cerenkov Effect. Electric field, Magnetic field, and Wavevector of electromagnetic wave in a LHM form a left-handed triad. LHMs support backward waves: anti-parallel group and phase velocity. Artificial effectively homogenous structure: metamaterial.

5 Rectangular Waveguide Filled with LHM P in k backward wave (v p = -v g ) ε>0, μ>0 k S ε<0, μ<0 k LH Triad S ε>0, μ>0 S P out HFSS simulation using effective medium [1] naturally occurring LH material has not yet been discovered

LHM Resonant Approach 1967: LHM were first proposed by Russian Physicist Victor Veselago 2001: LHM realized based on split ring resonators - Resonant Approach towards LHMs [2].

6 LHM Resonant Approach 1967: LHM were first proposed by Russian Physicist Victor Veselago 2001: LHM realized based on split ring resonators - Resonant Approach towards LHMs [2]. metal wire SRR SRR-based LHM unit-cell SRR: at resonance provides μ<0 metal wire: provides ε<0 SRR-based metamaterials only exhibit LH properties at resonance - inherently narrow-band and lossy. SRR-based LHMs are bulky - not practical for microwave engineering applications.

7 LHM Transmission Line Approach Backward wave transmission line can form a non-resonant LHM [3]-[4]. Transmission Line Approach is based on the dual of a conventional transmission line. C L C L C L L L L L Perfect LH transmission line Series capacitance (C L ) and shunt inductance (L L ) combination supports a fundamental backward wave. β = ω 1 C L L L Perfect LH transmission line not resonant dependent - low-loss and broad-band performance. However, perfect LH transmission line is not possible due to unavoidable parasitic righthanded (RH) effects occurring with physical realization.

8 Transmission Line Approach PRH TL L R PLH TL C L C R L L β = ω CL PRH R R β c ω +βc β PLH β c = ω ω 1 CL L L +β c β β

9 Composite Right/Left-Handed Metamaterial ω = βc 0 ω ω = +βc0 C L L R C R L L CRLH β = s ω 2 ( ) CRLR 2 1if ω < min( ωse, ωsh) s( ω) =, + 1if ω > max( ωse, ωsh) where ω se = ω C 1 L L R 1 + ω C and L ω L sh L = L L C 1 R L R L C + C L R L, Low frequencies: supports backward wave RH β High frequencies: supports forward wave Two cases Unbalanced: ω se ω sh Balanced: ω se = ω sh0

10 CRLH Metamaterial N p Homogeneity Condition CRLH TL Long wavelength regime p < λ g /4 0 L = N*p

11 CRLH Metamaterial Physical Realization C L L R capacitors C R L L inductor metal pads (provides RH effects) via to gnd Composite right/left-handed (CRLH) unit-cell Lumped element implementation Distributed microstrip implementation based on interdigital capacitor Distributed microstrip implementation based on Sievenpiper mushroom structure [5]

12 CRLH Implementation and Analysis Cascade periodic unit-cell to form one- or two-dimensional CRLH metamaterial TL. How to Characterize a CRLH Unit-Cell Propagation Constant Dispersion Diagram Impedance Bloch Diagram

Comparison of LHMs to PBGs and Filters Photonic Bandgap (PBG) Filters period Similarities periodic structures

PBG operated at frequencies where lattice period is multiple of λ g /2; LHMs operated at frequencies where

Similarities periodic structures based on low-pass/high-pass structures Differences Filters generally designed

13 Comparison of LHMs to PBGs and Filters Photonic Bandgap (PBG) Filters period Similarities periodic structures can be more than one-dimensional Differences PBGs have to be periodic; lattice period determines scattering PBG operated at frequencies where lattice period is multiple of λ g /2; LHMs operated at frequencies where period < λ g /4. Similarities periodic structures based on low-pass/high-pass structures Differences Filters generally designed to meet magnitude specifications; LHMs designed to meet both magnitude and phase. Node-to-node phase shifts of 180 required for filters. LHMs can be one-, two-, or threedimensional and are used as bulk mediums.

14 Dominant-Mode Leaky Wave Antenna

15 Leaky-Wave Antenna Theory Principle Conventional RH Leaky-Wave Antenna (operated at higher-order mode) CRLH Leaky-Wave Antenna [6] (operated at dominant mode) ω = βc 0 I LH GUIDANCE II LH RAD. ω III RH RAD. ω = +βc 0 IV RH GUIDANCE ω 0 β CRLH RH source z θ k o β θ = asin( βω ( ) k ) k z2 = k o2 - β 2 Characteristics: 0 k z Operating in leaky regions II : BACKWARD ( β < 0 ) III : FORWARD ( β >0) BROADSIDE radiation ( β = 0 ) balanced case: v g (β = 0 ) 0 Fundamental mode x

16 1-D Dominant Mode Leaky-Wave Antenna Design Specifications f o = 2.4 GHz Z B = 50 Ω 3-D Far-field Pattern for Several Frequencies unit-cell P in frequency beam scanning Backfire to Endfire

17 Design Flow Unit-cell parameter Design Guidelines Dispersion/Bloch Diagrams Driven Mode Optimize unit-cell for specifications Cascade unit-cells to form CRLH transmission line Simulate CRLH transmission line S-Parameters: matching Far-field: fast-wave region for leaky-wave application

18 Distributed unit-cell 1-D CRLH Unit-Cell (Interdigital) p series capacitance provided by interdigital capacitor shunt inductance provided from shorted stub shunt capacitance from top metal to ground plane series inductance from current on interdigital capacitor w l s l c Variables Initial Design Final Design unit-cell period stub length stub width interdigital finger length interdigital finger width spacing between fingers via radius substrate height substrate permittivity p l s w s l c w c S r h ε r 12.3 mm 10.0 mm 1.00 mm 10.5 mm 0.30 mm 0.20 mm 0.12 mm 1.57 mm mm 10.9 mm 1.00 mm 10.2 mm 0.30 mm 0.20 mm 0.12 mm 1.57 mm 2.2 via w s

19 1-D CRLH Unit-Cell Design Guidelines* For 2-D space scanning, we need to design a balanced (ω se = ω sh ) CRLH unitcell so that there is a seamless transition from LH to RH operation. 1. Choose center frequency, f o, which represents broadside radiation. (f o =2.4 GHz) 2. Calculate width required to obtain Z o, set w to this value. (w~5.0 mm) 3. Set stub width, w s, to 20% of w. (w s =1.0 mm) 4. Set stub length (l si =l s - w) to w; the electrical length of the stub has to be less than π/2. 5. Set the number of fingers, N, to 8 or 10. Then determine required w c and S=2w c /3. N=10 chosen. w c 5 3 w N mm 6. Calculate length of interdigital finger. l c λg 8 S c 8 f = 0.2 mm o o ε r 10.5 mm * Guidelines have been test on Rogers Duroid 5870 (er=2.33) and 5880 (er=2.2) for various substrate heights; for high permittivity substrate, the number of fingers should be reduced.

20 Dispersion/Bloch Diagram Extraction Design Specifications f o = 2.4 GHz Z B = 50 Ω extra section of mircostrip (5 mm each) Planar EM simulation S-Parameter extraction βp = cos 1 1 S11S22 + 2S21 S 12 S 21 Z B = (1 2 jzos21 sin( βp) S )(1 S ) S S 12

21 Dispersion Diagram Extraction Setup dispersion equation; this can be obtained directly from the S-parameters. βp = cos 1 1 S11S22 + 2S21 S 12 S 21 Go to Results > Create Report Then click on Output Variables

22 Dispersion Diagram Final Design Dispersion Diagram in Ansoft Designer fast-wave region beta < k o self resonance of interdigital capacitor air line slow-wave region beta > k o

23 Bloch Impedance Diagram Resulting Bloch Impedance Diagram in Ansoft Designer Re(Z B ) Im(Z B ) impedance (Ohm) LH fast-wave region RH fast-wave region

24 10-Cell CRLH Leaky-Wave Antenna Port1 Port2 Return/Insertion Loss Insertion loss Return loss LH fast-wave region RH fast-wave region

25 10-Cell CRLH Leaky-Wave Antenna Far-field Pattern for Several Frequencies Backward: f=1.95 GHz Broadside: f=2.35 GHz Forward: f=2.95 GHz

26 Small Metamaterial Antennas

27 Resonant Antenna Theory Conventional RH Patch Antenna (treat as periodic, consisting of 2 RH unit-cells ) CRLH Patch Antenna (2 CRLH unit-cells) RH RH p p resonance condition β = n nπ 2 p CRLH CRLH p p ω n = +1, +2, n=+1 n = 0, ±1, ±2, n=+1 n=-1 0 π/2 π CRLH can have same halfwavelength field distribution, but at much lower frequency βp

28 Frequency (GHz) GHz CRLH n=-1 Antenna [7] for 4 unit-cells Initial dispersion curve Increase L L Increase C L Increase C L & L L β ρ/π MIM Capacitance ground z CWP feed 12.2 mm y x 15 mm h 2 h 1 n= -1 mode is used h 1 = 3.16 mm h 2 = mm CPW stub 1/19λ 0 x 1/23λ 0 x 1/88λ 0

1.0 GHz CRLH n=-1 Antenna [7] Return Loss (db) 0-5 -10 n = -3 n = -2 top view 180-15 -20-25 135 n = -1 measurement HFSS 0 0.5 1 1.5 2 2.5 3 3.5 4 4.

29 1.0 GHz CRLH n=-1 Antenna [7] Return Loss (db) n = -3 n = -2 top view n = -1 measurement HFSS Frequency (GHz) E-copol (x-z plane) H-copol (y-z plane) E-xpol (x-z plane) H-xpol (y-z plane) back view

30 CRLH n=0 Antenna (Monopolar) [8] Experimental Results ω βc 0 ω = ω = +βc0 Peak Gain (dbi) 4 2 Exp. Peak Gain Exp. Resonant Frequency Frequency (GHz) n=0 points # of unit-cells (N) As N increases CRLH RH β Gain increases. Resonant frequency does not change much.

0 330 30 0-10 300-20 CRLH n=0 Antenna (Monopolar) -30-40 270 90-30 -20-10 240 120 z 0 330 30 0-10 60 300-20 x z x y -30-40 270 90-30 -20-10 240 120 0 210 150 num. 0 210 150 num. 180 exp.

31 CRLH n=0 Antenna (Monopolar) z x z x y num num. 180 exp. 180 exp. z 60 y x num. 180 exp. 60 y Θ, φ x-z plane y-z plane x-y plane Cross-Pol 90

32 Dual-/Multi-Band Metamaterial Components

33 Dual-Band Hybrid Coupler 1 CRLH / CRLH hybrid [9] CRLH 2 CRLH CRLH 4 CRLH 3 Characteristics: dual-band functionality for an arbitrary pair of frequencies f 1, f 2 principle: transition frequency (f o ) provides DC offset additional degree of freedom with respect to the phase slope applications in multi-band systems f 0 Conventional quadrature: restricted to odd harmonics because only control on slope DC offset f 1 CRLH f2 CRLH f = 3 f conv 2 1 f conv. RH

34 Dual-Band Hybrid Coupler in isolated Branch Line LH TLs Z 0 2 Z 0 Z 0 Z 0 2 Band # 1: 0.92 GHz Band # 2: 1.74 GHz out out S-parameters (db) Experimental Results f f 2 1 = 1.89 S11 S21 S31 S frequency (GHz)

35 Negative Refractive Index Lenses

$Negative Refractive Index Flat Lens [10] (n LH )sinθ LH = (n RH ) sinθ RH Effective medium HFSS simulation LHM RHM source (15 mm from interface) θ RH θ LH RH$

36 Negative Refractive Index Flat Lens [10] (n LH )sinθ LH = (n RH ) sinθ RH Effective medium HFSS simulation LHM RHM source (15 mm from interface) θ RH θ LH RH medium LH medium refractive index n RH > 0 refractive index n LH < 0 Possibility of realizing a flat lens E-field magnitude RH medium RH medium 1 LH medium RH medium 2

Two-Dimensional CRLH Realization Based on Sievenpiper High-Impedance Structure patch p period of unit cell p C R L R L L C L via ground plane How to obtain dispersion

37 Two-Dimensional CRLH Realization Based on Sievenpiper High-Impedance Structure patch p period of unit cell p C R L R L L C L via ground plane How to obtain dispersion characteristics? 1. Drivenmode Approach Simple, quick, 1-D dispersion diagram. 2. Eigenmode Approach Requires more processing time, accounts for mode coupling, 2-D dispersion diagram.

38 Unit-Cell Setup: Physical Details metal patch metal via radius = 0.12 mm height = 1.27 mm t=4.8 mm t=4.8 mm h=1.27 mm p=5.0 mm p=5.0 mm z substrate parameters ε r =10.2, tanδ= Np/m ground plane x y * patch,via, and ground plane are assigned as copper.

39 Design Flow Unit-Cell Parameters 1 st Order Calculation Design Dispersion Characteristics Driven Mode Approach 1-D dispersion No mode coupling Verify Eigen Mode Approach 2-D dispersion Mode coupling Flat Lens Realization Phase Matching HFSS Simulation Flat Lens Symmetry Conditions: Reduce Simulation Time Field Plots: Magnitude & Phase

40 Sievenpiper Unit-Cell: 1 st Order Calculation distributed unit-cell equivalent circuit model f sh = 1/{2πsqrt(C R x L L )} series capacitance: C R ~ substrate permittivity x (patch area/substrate height) shunt inductance: L L ~ 0.2 x substrate height x ln[(2 x substrate height/via radis) 1] * Left-handed mode will always occur below the shunt resonance (ω sh ). Therefore, design dimensions such that w sh occurs at higher limit of frequency of interest. f sh ~ 5 GHz for the dimensions shown in previous slide.

41 Sievenpiper Unit-Cell: Driven Mode Port 1 via gap=0.2 mm Port 2 Modify unit-cell so that ports can be placed on it, while keeping dimensions the same. Unit-cell becomes asymmetrical. Run driven mode solution; set mesh frequency to ω sh from 1 st order calculation. p=5.0 mm Obtain S-parameters, use following expression to calculate propagation constant.

42 Sievenpiper Unit-Cell: Driven Mode 1-D dispersion diagram (from Port 1 to Port 2) air line right-handed mode band-gap left-handed mode

Eigenmode Solver: 2-D Dispersion Diagram z Γ x Γ to X: px=0, py=0 180 y X X to M: px=0 180, py=180 M M to Γ : px, py: 0 180 px:

43 Eigenmode Solver: 2-D Dispersion Diagram z Γ x Γ to X: px=0, py=0 180 y X X to M: px=0 180, py=180 M M to Γ : px, py: px: phase offset in x-direction py: phase offset in y-direction Use Linked Boundary Conditions (LBCs) in HFSS to apply required phase shifts.

44 Sievenpiper Unit-Cell Setup Airbox and PML Setup 1. Create airbox1. 2. Select top face of airbox1 and assign PML. 3. Create airbox2. PML h PML =2.50 mm airbox2 airbox1 h airbox1 =8.00 mm z physical dimensions shown in previous slide x y

45 Unit-Cell Setup: Linked Boundaries XZ - Planes YZ - Planes sx mx z my sy x Slave BC: sx phase delay: px (180 deg) y Slave BC: sy phase delay: py (0 deg)

46 Eigenmode 2-D Dispersion Diagram 5 Plotted in Microsoft Excel frequency (GHz) Γ X M Γ

47 Dispersion Comparison: 1-D vs 2-D Solve 8 frequency (GHz) Drivenmode Eigenmode (2D) Beta*p (deg) Use drivenmode to quickly characterize/design, eigenmode to verify

48 Flat Lens Physical Realization Entire circuit on Roger RT 6010 substrate with ε r = 10.2 and h = 1.27mm 40.0 mm PPWG (n = +3.2) voltage source 15 mm refocus should occur at 3.8 GHz 50.0 mm LHM based on 21x10 mushroom unit-cells (n = 3.8 GHz) 40.0 mm PPWG (n = +3.2) mm

49 Flat Lens Phase Matching Condition 5 frequency (GHz) phase match at 3.8 GHz βp = 72 deg, n =3.2 X M 0 Γ βp (deg)

Flat Lens Simulation Setup Entire circuit on Roger RT 6010 substrate with ε r = 10.2 and h = 1.27mm 130.

8 GHz) Boundary Conditions Radiation boundary applied on Top and Side A, B, and C of air box.

50 Flat Lens Simulation Setup Entire circuit on Roger RT 6010 substrate with ε r = 10.2 and h = 1.27mm mm voltage source 62.5 mm C D PPWG (n = +3.2) 18.0 mm A B LHM based on 21x10 mushroom unit-cell (n = 3.8 GHz) Boundary Conditions Radiation boundary applied on Top and Side A, B, and C of air box. Finite conductivity (Copper) applied on bottom of airbox, PPWG trace, and mushroom patches. Symmetry boundary (perfect-h) applied to Side D to reduce problem size.

51 Flat Lens Field Calculator for Phase To plot the E-field phase, the field calculator has to be used. Go to HFSS > Fields > Calculator Since the field is quasi-tem, only the z-component of the E-field is required. Quantity > E Scal? > ScalarZ Vec? > VecZ Complex > CmplxPhase Mag Add, give name PhazeZ

52 Flat Lens E-Field Plots (Ground Plane) field on ground f=3.75 GHz Magnitude Phase

53 Flat Lens E-Field Plots (Above Structure) field on top of f=3.75 GHz (3.5 mm above top metal) Magnitude Phase

54 Flat Lens Experimental Results f 0 =3.79 GHz E-field magnitude Source Source E-field phase E-field measured ~ 3.5 mm above CRLH region

55 Future Trends

11n Application [11] Active CRLH Metamaterials High-gain

56 Applications & Research Metamaterial Multiple-Input-Multiple-Output (MIMO) Arrays for n Application [11] Active CRLH Metamaterials High-gain leaky-wave antennas (embed amplifiers in unit-cell) [12] Distributed amplifiers [13] Tunable Phase Shifters [14]

cylindrical DRs in TE mode cutoff parallel plate waveguide

57 Implementations Nano-Metamaterials: optical frequency applications [15] Evanescent-Mode Metamaterials [16] 1-D LHM: cylindrical DRs in TE mode cutoff parallel plate waveguide (-ε) H-field Profile (TE 01δ mode, -μ) Three-Dimensional Metamaterials [17]

58 Summary Left-Handed Metamaterial Introduction Resonant approach Transmission line approach Composite Right/Left-Handed Metamaterial Metamaterial-Based Microwave Devices Dominant leaky-wave antenna Small, resonant backward wave antennas Dual-band hybrid coupler Negative refractive index flat lens Future Trends

59 References 1) C. Caloz, C.C. Chang, and T. Itoh, Full-wave verification of the fundamental properties of left-handed materials (LHMs) in waveguide configurations, J. App. Phys., vol. 90, no. 11, pp , Dec ) R.A. Shelby, D.R. Smith, and S. Schultz, Experimental verification of a negative index of refraction, Science, vol. 292, pp , Apr ) A. Lai, C. Caloz, and T. Itoh, Composite right/left-handed transmission line metamaterials, IEEE Microwave Magazine, Vol. 5, no. 3, pp , Sep ) C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications, Wiley and IEEE Press, Hoboken, NJ, ) D. Sievenpiper, L. Zhang, R.F.J. Broas, N.G. Alexopolous, and E. Yablonovitch, High-impedance surface electromagnetic surfaces with a forbidden frequency band, IEEE Trans. Microwave Theory Tech., vol. 47, no. 11, pp , Nov ) L. Liu, C. Caloz, and T. Itoh, Dominant mode (DM) leaky-wave antenna with backfire-to-endfire scanning capability, Electron. Lett., vol. 38, no. 23. pp , Nov ) C.J. Lee, K.M.K.H. Leong, and T. Itoh, Design of resonant small antenna using composite right/left-handed transmission line, Proc. IEEE Antennas and Propagation Society Int. Symp., Washington D.C., Jun ) A. Lai, K.M.K.H. Leong, and T. Itoh, Infinite wavelength resonant antennas with monopolar radiation patterns based on periodic structures, IEEE Trans. Antennas Propag., vol. 55, no. 3, pp , Mar ) I. Lin, C. Caloz, and T. Itoh, A branch-line coupler with two arbitrary operating frequencies using left-handed transmission lines, IEEE-MTT Int. Symp. Dig., Philadelphia, PA, Jun. 2003, vol. 1, pp ) A. Lai, Theory and design of composite right/left-handed metamaterial-based microwave lenses," Master Thesis, Dept. E. E., UCLA, Los Angeles, CA, ) Rayspan Corporation, 12) F. P. Casares-Miranda, C. Camacho Peñalosa, and C. Caloz, High-gain active composite right/left-handed leaky-wave antenna, IEEE Trans. Antennas Propag., vol. 54, no. 8, pp , Aug ) J. Mata-Conteras, T. M. Martìn-Guerrero, and C. Camacho-Peñalosa, Distributed amplifiers with composite right/left-handed transmission lines, Microwave Opt. Technol. Lett., vol. 48, no. 3, pp , March ) E.S. Ash, Continuous phase shifter using ferroelectric varactors and composite right-left handed transmission lines, Master Thesis, Dept. E.E., UCLA, Los Angeles, CA ) V.A. Podolskiy, A.K. Sarychev, and V.M. Shalaev, Plasmon modes in metal nanowires and left-handed materials, J. Nonlin. Opt. Phys. Mat., vol. 11, no. 1, pp , ) T. Ueda, A. Lai, and T. Itoh, Demonstration of negative refraction in a cutoff parallel-plate waveguide loaded with 2-D square lattice of dielectric resonators, IEEE Trans. Microwave Theory Tech., vol. 55, no. 6, pp , Jun ) M. Zedler, P. Russer, and C. Caloz, Circuital and experimental demonstration of a 3D isotropic LH metamaterial based on the rotated TLM scheme, IEEE-MTT Int'l Symp., Honolulu, HI, Jun

$Antenna Ansoft HFSS: Negative Refractive Index$

60 Design Guide Ansoft Designer: 1-D Leaky-Wave Antenna Ansoft HFSS: Negative Refractive Index Flat Lens

ON THE STUDY OF LEFT-HANDED COPLANAR WAVEGUIDE COUPLER ON FERRITE SUBSTRATE

Progress In Electromagnetics Research Letters, Vol. 1, 69 75, 2008 ON THE STUDY OF LEFT-HANDED COPLANAR WAVEGUIDE COUPLER ON FERRITE SUBSTRATE M. A. Abdalla and Z. Hu MACS Group, School of EEE University